The home team seldom got out of second gear, but five minutes after coming on the Polish striker slid home Lee Naylor's cross.
Up to that stage Aberdeen lying joint second in the League appeared content to settle for the draw, but it took a marvellous save by Celtic keeper Artur Boruc in the last minute to deny the visitors a share of the points.
This result increased Celtic's stranglehold at the top of the SPL to 16 points prior to their Champions League visit to Copenhagen.
Celtic went close in the opening stages with a series of headers from Stephen McManus, Jiri Jarosik and Thomas Gravesen which slid just wide of the post.
Aberdeen keeper James Langfield did well to parry out Gravesen's powerful effort, but the visitors only tested Boruc once in the first half with a shot from Chris Clark.
Celtic should have taken the lead just before half-time when Naylor's powerful strike was pushed out by Langfield, but Kenny Miller blasted the rebound wide from only six yards.
At the start of the second half Shunsuke Nakamura's 30-yard free-kick drifted narrowly wide and Aiden McGeady's shot was too near Langfield.
Just when it looked as though Celtic were running out of ideas Zurawski latched on to Naylor's clever cross and turned Russell Anderson before shooting home.
Celtic should have increased their lead but Miller and Zurawski spurned further chances.
The home team nearly paid the penalty when Barry Nicholson's free-kick was met by Anderson, but the central defender's powerful header was brilliantly touched over by Boruc.